BBM方程的全离散混合有限元方法  

A Fully Discrete Mixed Finite Element Method for the Benjamin-Bona-Mahony(BBM) Equation

作　　者：覃燕梅[1] 孔花[1] 罗丹[1] 冯民富[2] 

机构地区：[1]四川省高等学校数值仿真重点实验室/内江师范学院数学与信息科学学院,内江641112 [2]四川大学数学学院,成都610054

出　　处：《应用数学学报》2015年第4期597-609,共13页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(11271273);四川省教育厅青年基金项目(11ZB175)

摘　　要：将混合有限元法应用到BBM方程,对高维BBM方程建立了半离散化和全离散化有限元格式.空间采用最常用的连续多项式有限元P_m/P_(m-1)(m≥1)逼近,时间采用向后欧拉差分离散.证明了有限元解的存在唯一性,并对收敛性进行了详细的分析,得出了最优的误差估计.最后,通过数值算例对该方法的稳定性和收敛性进行了验证.In this article, the semi discrete and fully discrete schemes for the Benjamin- Bona-Mahony （BBM） equation are proposed by mixed finite element method. The fully discretization in space is based on the continuous finite elements Pm/Pm-1（m ≥ 1）, for the time discretization the backward Euler scheme is used. The existence and uniqueness of the mixed generalized solution are given. The convergence of semi discrete and fully discrete mixed finite element solutions is proved. The error estimation results show that the method achieves optimal accuracy with respect to solution regularity. The numerical results were given, which demonstrate the stability and convergence of the method presented.

关 键 词：BBM方程 混合有限元法 误差分析 

分 类 号：O242.21[理学—计算数学]